Dynamic Stress Ratio Research Articles

Fractional Order Derivative Kelvin Model of Cumulative Pore Pressure under Cyclic Loading

The settlement caused by traffic loading on soft ground has serious effects on subways, tunnels and highway bridges. Therefore, it is important to study the long-term settlement caused by traffic loading. A series of undrained cyclic triaxial tests was conducted on saturated soft clay that involved different initial effective confining pressures, dynamic stress ratios and consolidation modes. The relationship between cumulative pore pressure and cyclic times was obtained. The general Kelvin model and the fractional-order derivative Kelvin model were used to simulate this relationship. Simultaneously, the genetic algorithm was used to optimize the parameters of these two models. When comparing the calculation and test values, it is verified that the general Kelvin model can simulate the cumulative pore pressure only when the dynamic stress ratio is small, and the fractional-order derivative Kelvin model is more suitable for simulating the cumulative pore pressure under cyclic loading.

Study on seismic residual deformation test of reinforced soil

The reinforced material can increase the stability of soil material, improve its shear strength and reduce the residual deformation. In this paper, the vibration triaxial tests of coarse-grained soil under different confining pressure, consolidation ratio and dynamic stress are carried out by using the 100t electro-hydraulic servo large-scale static and dynamic triaxial testing machine of Institute of Water Resources and Hydropower Research. The results show that the average reduction ratio of the axial residual deformation of reinforced soil to that of unreinforced soil is 40%-50%, and the average reduction of the volumetric residual deformation is 30-40% It has a good inhibitory effect. With the increase of confining pressure, consolidation ratio and dynamic shear stress ratio, the axial residual deformation and volumetric residual deformation of reinforced soil increase in varying degrees. The reinforcement effect of geogrid material on soil sample under different conditions is analyzed. The lower the dynamic shear stress ratio and the higher the consolidation ratio, the better the reinforcement effect. The lower the confining pressure is, the lower the reduction ratio of the reinforcement to the volumetric strain is.

A dynamic strength criterion for frozen sulfate saline silty clay under cyclic loading

The strength properties of frozen saline soils under cyclic loading are more complex than those of unfrozen soils and frozen salt-free soils due to the existence of salt crystals in soil matrix. In this paper, a serious of tri-axial cyclic loading tests are conducted for frozen sulfate saline silty clay (FSSSC) with different Na2SO4 contents under different confining pressures and loading dynamic stress ratios at the temperature of −6 °C, respectively. The experimental results illustrate that the dynamic strength of FSSSC decreases with the increase of axial strain. The critical state line of FSSSC under cyclic loading is moving constantly. The dynamic critical state lines of FSSSC with different salt contents are different under same axial strains. The dynamic friction angle of FSSSC is related to salt content, loading dynamic stress ratio and confining pressure. Based on the experimental results, a dynamic strength criterion for FSSSC under cyclic loading is proposed, and the method of determining dynamic strength parameters is given. This strength criterion not only can reflect the effect of loading dynamic stress ratio and salt content on dynamic strength, but also can describe the influence of high confining pressure on dynamic strength.

Analytical Study of the Effect of NaCl Solution on Fatigue Resistance of Rotating Shafts

Dynamic shafts subjecting to salty rain water, especially in places with no rain water drainage networks, is undesirable because this media causes corrosion of the parts of shaft that increases as increasing of shaft immersion in a salty media (NaCl) also, increasing of concentration which in turns reducing number of operation runs. Increasing salt concentration from 3% to 6% NaCl results in decreasing of operation runs from 25600 to 17100 runs. Also, increasing salt concentration leads to raise the effect of alternating stress that makes strain hardening factor drop to 0.45 and ratio of dynamic shear stress to static one raise to 2.44 that affects shaft metal performance to resist fatigue. Samples were also, treated by oxy acetylene surface hardening and were cooled by immersion in oil then immersion in 6% NaCl salty solution, the results showed that number of operation runs before failure had increased up to 71022, the effect of alternating stress had decreased down to 6100 N/m2, surface strain hardening factor had increased up to , also ratio of dynamic shear stress to static one had decreased down to 0.839. This is a good indicator of the effectiveness of surface hardening process of shaft parts that subject to salty rain water during maintenance operations.

Experimental Research on Deformation Characteristics of Using Silty Clay Modified by Oil Shale Ash and Fly Ash as the Subgrade Material after Freeze-Thaw Cycles

To achieve the purposes of disposing industry solid wastes and enhancing the sustainability of subgrade life-cycle service performance in seasonally frozen regions compared to previous research of modified silty clay (MSC) composed of oil shale ash (OSA), fly ash (FA), and silty clay (SC), we identified for the first time the axial deformation characteristics of MSC with different levels of cycle load number, dynamic stress ratio, confining pressure, loading frequency, and F-T cycles; and corresponding to the above conditions, the normalized and logarithmic models on the plastic cumulative strain prediction of MSC are established. For the effect of cycle load number, results show that the cumulative plastic strain of MSC after 1, 10, and 100 cycle loads occupies for 28.72%~35.31%, 49.86%~55.59%, and 70.87%~78.39% of those after 8000 cycle loads, indicating that MSC possesses remarkable plastic stability after 100 cycles of cycle loads. For the effect of dynamic stress ratio, confining pressure, loading frequency, and F-T cycles, results show that dynamic stress ratio and F-T cycles are important factors affecting the axial deformation of MSC after repeated cycle loads; and under the low dynamic stress ratio, increasing confining pressure and loading frequency have insignificant effect on the axial strain of MSC after 8000 loads. In term of the normalized and logarithmic models on the plastic cumulative strain prediction of MSC, they have a high correlation coefficient with testing data, and according to the above models, the predicted result shows that the cumulative plastic strain of MSC ranges from 0.38 cm to 2.71 cm, and these predicted values are within the requirements in the related standards of highway subgrades and railway, indicating that the cumulative plastic strain of MSC is small and MSC is suitable to be used as the subgrade materials.

Numerical study of dynamic stress developed in the high speed rail foundation under train loads

As a ground treatment method, geosynthetic-reinforced pile foundation (GRPF) is widely applied in the railway construction, especially in high-speed railway (HSR), due to the strict restrictions on post-construction settlement. The post-construction settlement is commonly considered induced by the weight of railway structure as well as the moving train load. Therefore, the dynamic stress developed in the GRPF induced by HSR is important for the post-construction settlement study. However, most studies focus on the dynamic stress on the track and subgrade, studies concerning dynamic stress in GRPF are few. In this paper, a three-dimensional time-domain viscoelastic finite element method (FEM) model is developed to study the dynamic response of GRPF under the high-speed rail load. The simulation model is verified by a comparison with the results of analytical solution. And based on this model, parameter study is conducted. The investigation of train speed and the pile group layout has shown that the dynamic stress amplitude significantly increases after the train speed reaches the Rayleigh wave velocity of the subgrade, while the pile-soil stress acts reversely. For the influence of the pile group layout, three variables: pile cap size, longitudinal pile spacing, and lateral pile spacing are studied respectively. A parametric study of pile cap size, longitudinal pile spacing and lateral pile spacing have suggested that the amplitude of dynamic stress developed in the soil is more susceptible to the pile spacing rather than pile cap size. Besides, increasing replacement ratio results in the decrease of dynamic pile-soil stress ratio.

Amplitude Ratio Effect on Dynamic Characteristics of Remolded Soft Clay Under Train Loads

A hollow cylinder apparatus was used to simulate the stress paths induced in traffic-affected ground. A series of undrained shear tests was carried out. The inflection points on generalized shear strain curves were used to establish a damage criterion, which distinguished different damage characteristics under different stress levels. Tests were carried out to elucidate the effect of different initial deviator stress on soil shear stiffness. The variation of shear modulus with vibration times under different dynamic stress ratios was analyzed. Stiffness degradation and plastic cumulative deformations of soil were analyzed for the case where the initial deviator stress was equal to zero. The prediction models models can be used to investigate stiffness degradation patterns and axial plastic cumulative deformation patterns.

Settlement of Soft Clay Subgrade Under Coupled Effects of Vibration Frequency and Dynamic Stress Ratio Caused by High-Speed Train Loads

Settlement regularity of soft clay subgrade under cyclic principal stress rotation caused by high-speed train loads is investigated. In laboratory tests, it is found that, with increasing vibration frequency at a fixed dynamic stress ratio, the increase of axial plastic cumulative strain in saturated soil is restricted at mid-high frequencies (0.5-2 Hz), and the changes in pore-water pressure are not evident. Combined with the empirical settlement formula and analysis of the dynamic amplification equation of German standard, a simplified settlement calculation method accounting for resonance is obtained.

Influence of principal stress rotation of unequal tensile and compressive stress amplitudes on characteristics of soft clay

Soil behavior can reflect the characteristics of principal stress rotation under dynamic wave and traffic loads. Unequal amplitudes of tensile and compressive stresses applied to soils have complex effects on foundation soils in comparison with the pure principal stress rotation path. A series of undrained cyclic hollow torsional shear tests were performed on typical remolded soft clay from the Ilexi area of Nanjing, China. The main control parameters were the tensile and compressive stress amplitude ratio (α) and the cyclic dynamic stress ratio (η). It was found that the critical η tended to remain constant at 0.13, when the value of the compressive stress amplitude was higher than the tensile stress amplitude. However, the influence of the tensile stress was limited by the dynamic stress level when α= 1. For obvious structural change in the soil, the corresponding numbers of cyclic vibration cycles were found to be independent of α at low stress levels and were only related to η. Finally, a new method for evaluating the failure of remolded soft clay was presented. It considers the influence of the tensile and compressive stresses which caused by complex paths of the principal stress rotation. This criterion can distinguish stable, critical, and destructive states based on the pore-water-pressure-strain coupling curve while also providing a range of failure strain and vibration cycles. These results provide the theoretical support for systematic studies of principal stress rotation using constitu tive models.

Leaning pagodas in China: laboratory test and analysis of subsidence under frequent earthquakes

The inclination of ancient pagodas leads to a non-uniform stress distribution on the soil below. This non-uniform stress threatens the structural stability of the ancient pagodas, and the degree of damage depends on the soil properties. This paper researches the residual strain under the ancient pagodas in China to simulate the non-uniform stress state under frequent earthquake conditions using a dynamic triaxial test apparatus. The non-uniform stress state was expressed by the consolidation stress ratio. The frequent earthquakes were indicated by the dynamic stress ratio and cyclic interval vibration loading. To describe the foundations of the ancient pagodas in China, two types of soil, the mucky clay (Q4) and the paleo-clay ( $${\text{Q}}_{3}^{\text{al}}$$ ), were tested. The relationship between the two different soils and the consolidation and dynamic stress ratios were determined by measuring the deformation and accumulated deformation. Additionally, mathematical models to estimate the residual strains of the soils were established and verified. The results indicate that the soil strain increment of mucky clay, which increases with the consolidation stress ratio and dynamic stress ratio, is an important parameter for evaluating the leaning pagodas’ stability in soft soil regions when subjected to frequent earthquake. The soil strain increment of paleo-clay, however, is inversely proportional to the consolidation stress ratio and no apparent relationship is found with the dynamic stress ratio. More research needs to be done on the subsidence of paleo-clay.

Particle Flow Simulation on Collapse Characteristics of Silt Under Mutation of Principal Stress Orientation

The behaviors of granular material and influencing factors under complex dynamic loading are studied by more and more researchers with particle flow method. Only the strain-controlled loading has been generally used in the current study, although this method was not consistent with the practice of engineering in many situations. In this article, stress-controlled dynamic simulation tests were carried out with particle flow method, which were used to study the collapse characteristics of silt under mutation of principal stress orientation. The tests were performed by PFC2D. The simulation results and the laboratory real tests’ results had a high degree of similarity, particularly in the collapse strain and vibration times. It was very useful to forecast the silt's critical failure state. Based on the verification data, the effects of confining pressure and cyclic shear stress ratio on the collapse characteristics of silt were studied further. With the increase of cyclic shear stress ratio, the deviator strain amplitude increased and the required vibration times gradually reduced to achieve the same strain level. Under the same dynamic shear stress ratio and vibration times, the initial dynamic elastic modulus slightly increased with the increase of initial confining pressure, and the variation range of final collapse deviator strain was small. In the analysis of micro-structural evolution, the redistribution of internal stress of sample was revealed during cyclic loading. With the increase of vibration times, the development of distribution gradually stabilized, and then the high shear stress appeared in some connected regions. On that stage, the particle system developed to instability and failure. The PFC simulation results confirmed that the collapse state was the critical stage to trigger the liquefaction of silt.

The Generalized Dynamic Factor of Hydraulic Excavator Working Device

Synchronous test platforms were built to test the dynamic stress and working device attitude. The dynamic stress spectrums of all the test points under a variety of common conditions were obtained. The digging gestures corresponding to the peak of the dynamic stress spectrums were found out and taken as the specified digging gestures for the calculation of the static stress. The static stress nephogram of working device under the specified digging gestures was calculated using traditional static strength analysis. By conducting statistical analysis on the ratio of dynamic stress and static stress of all the testing points. Then, the range of generalized dynamic factor of working device was obtained.

Dynamic deformation behaviour of coarse aggregate under cyclic loading by PFC3D

Dynamic deformation behaviours of soil measured by resonant column tests or cyclic triaxial tests are very important in dynamic response analyses. This paper presents the Particle Flow Code in three-dimensional analysis of dynamic deformation behaviours of coarse aggregate under both Single-Direction Vibration (SDV) and Multi-Direction Vibration (MDV) conditions. The numerical model of coarse aggregate is presented, and the desired porosity is obtained by a radius expansion method. It has been found from this research that the dynamic shear modulus under MDV condition is larger than that under SDV condition under the same dynamic shear strain. The damping ratio obeys the same law. The maximum dynamic shear modulus and the maximum dynamic shear stress ratios of MDV and SDV are 1.35 and .98, respectively. Both the normalised dynamic shear modulus and damping ratio vs. normalised dynamic shear strain have the same trend for different cyclic loading methods. According to the energy analysis, particles do not always slide under cyclic loading. When the strain energy approaches the original state from the maximum or minimum strain energy, particles do not slide. In order to simulate the real material dynamic deformation behaviour, the relationship between microscopic parameters and dynamic shear modulus and damping ratio are studied and a calibration procedure of microscopic parameters is proposed.

An Experimental Study on the Dynamic Strength of Earth-Rock Aggregate

This paper, based on dynamic triaxial apparatus of GDS, makes a consolidated undrained dynamic triaxial test of the saturated earth-rock aggregate of different earth-rock ratio, analyzes its processes and results, and preliminary discusses the influence of confining pressure, dynamic stress and earth-rock ratio on the dynamic strength of sandy pebble soil samples. Therefore, it providess some cognition of the study of earth-rock aggregate.

On the Propagation of Slip Fronts at Frictional Interfaces

The dynamic initiation of sliding at planar interfaces between deformable and rigid solids is studied with particular focus on the speed of the slip front. Recent experimental results showed a close relation between this speed and the local ratio of shear to normal stress measured before slip occurs (static stress ratio). Using a two-dimensional finite element model, we demonstrate, however, that fronts propagating in different directions do not have the same dynamics under similar stress conditions. A lack of correlation is also observed between accelerating and decelerating slip fronts. These effects cannot be entirely associated with static local stresses but call for a dynamic description. Considering a dynamic stress ratio (measured in front of the slip tip) instead of a static one reduces the above-mentioned inconsistencies. However, the effects of the direction and acceleration are still present. To overcome this we propose an energetic criterion that uniquely associates, independently on the direction of propagation and its acceleration, the slip front velocity with the relative rise of the energy density at the slip tip.

Deep-seated downslope slip during strong seismic shaking

[1] Strong seismic waves cause frictional failure within regolith on hillslopes. The material responds anelastically to the combined oscillating dynamic and static gravitational stresses. Gravity drives preferential downslope movement of the transiently weakened material. The net effect over many earthquake cycles is a tens of meter thick slow landslide, that is a sackung. The classical approach to hillside failure involves downslope dynamic accelerations or equivalently downslope dynamic shear tractions. Rate and state friction quantifies that the starting coefficient of friction is a few tenths higher that the apparent long-term coefficient of friction from the angle of repose, 0.96–1.25 in the calculations, retaining an extra digit. Furthermore, the dynamic Coulomb stress ratio for dynamic to lithostatic stress for S-waves refracted toward vertical paths is the dynamic acceleration in g's above the scale depth 1/k, the inverse of the wave number. In more detail, a dynamic acceleration of 0.13–0.35 g destabilizes slopes near the angle of repose. Seismologists expect such acceleration near active major faults, compatible with the widespread occurrence of sackungen on steep slopes. Accelerations of 0.96–1.25 = ∼1 g destabilize shallow slopes, leading to net downhill movement, analogous to the movement of an object down a vibrating ramp. However, sackungen are rare or even absent on shallow slopes in California indicating the rarity of sustained 1 g accelerations. A second mechanism may drive downhill movement on modest ∼19° slopes as observed in the San Gabriel Mountains of California near the San Andreas Fault. The near-field velocity pulse on strike-slip faults produces only a few tenths g acceleration but particle velocities of over 1 m s−1 persisting over >1 s. Dynamic stresses and strains scale with this velocity and extend all the way to the free surface. Coulomb failure criteria are exceeded at shallow depths. Failure greatly weakens the regolith allowing it to move downhill in response to gravity. This mechanism appears capable of producing prehistoric 1 m per event slip on modest slopes observed in the San Gabriel Mountains.

Dynamic Response Analysis on Efficacy of CFG-Pile in Different Height Embankment

In order to analyze the effect of embankment height to dynamic stability, Cross-section in the Beijing-Shanghai high-speed railway is chosen and the numerical simulation calculation method is applying. Distributing rules of dynamic displacement and dynamic stress of the subgrade surface and ground surface, attenuation rules of dynamic response and dynamic stress ratio between pile and soil on the vertical section were studied. It shows that the dynamic stress of pile and soil generally attenuates in depth and attenuation of dynamic stress ratio between pile and soil mostly concentrates into the scope of 10 meters beneath the ground. Moreover, with the increment of embankment height and attenuation of dynamic stress in direct proportion to the depth, the dynamic stress transferring to ground surface decrease and the dynamic displacement of ground surface minish. As a result, the scheme of CFG-pile with 3m scheme is superior to that of 2m scheme for enhancing dynamic stability and reducing dynamic displacement and stress in low embankment. It will be instructive to control design and construction for the low embankment in Beijing-Shanghai high-speed railway.

The Effect of CFG-Pile Caps and Cushion to Stability of Embankment

Subgrade diseases are exposed more and more serious with raising speed of existing railway in wide range. Dynamic numerical simulation had been done to analyze the effect of CFG-pile caps and cushion in composite foundation with CFG-pile in low embankment of Beijing-Shanghai high-speed railway. Distribution rules of dynamic displacement and dynamic stress of the subgrade surface and ground surface on the cross section, attenuation rules of dynamic response and dynamic stress ratio between pile and soil on the vertical section were studied. It shows that the dynamic stress of pile and soil generally attenuates in depth and attenuation of dynamic stress ratio between pile and soil mostly concentrates in the scope of 10m beneath the ground and dynamic stress caused by train load is undertaken by the pile. Moreover the scheme of CFG-pile with no pile caps and rigid cushion scheme is superior to that of pile caps and flexible cushion scheme for enhancing dynamic stability and reducing dynamic displacement and stress in low embankment. It will be instructive to control design and construction for the low embankment in Beijing-Shanghai high-speed railway.

The mitigation negative effect of tunnel-blasting-induced vibrations on constructed tunnel and buildings

Provided the results of a research conducted to investigate the relationships between the empirical vibration attenuation equation of Peak Particle Velocity (PPV) and the Scaled Charge (SC) through testing the blasting-induced vibrations on the spot of Wanshishan tunnel based on 96 vibration recordings. It is found that the maximum charge amount per delay in Wanshishan tunnel excavating is determined by the buildings on the surface and the constructed tunnel nearby. Considering that the repeated blast loading in tunnel blasting caused accumulative effects of damage on buildings, comfortable threshold damage limits of PPV to maintain buildings safety was given. Dynamic Stress Ratio (DSR) was adopted to study the stability of constructed tunnel on the action of blasting induced vibrations. The method to determine specific maximum charge amount per delay in Wanshishan tunnel excavation was given. It is proved that the findings in this study are very effective to control the negative effects of blasting-induced vibrations on buildings on the surface and constructed tunnel nearby.

Pore water pressure increment model for saturated Nanjing fine sand subject to cyclic loading

Three groups of dynamic triaxial tests were performed for saturated Nanjing fine sand subjected to uniform cyclic loading. The tested curves of the excess pore water pressure (EPWP) ratio variation with the ratio of the number of cycles are provided. The concept of the EPWP increment ratio is introduced and two new concepts of the effective dynamic shear stress ratio and the log decrement of effective stress are defined. It is found that the development of the EPWP increment ratio can be divided into three stages: descending, stable and ascending. Furthermore, at the stable and ascending stages, a satisfactory linear relationship is obtained between the accumulative EPWP increment ratio and natural logarithm of the effective dynamic shear stress ratio. Accordingly, the EPWP increment ratio at the number of cycles N has been deduced that is proportional to the log decrement of effective stress at the cycle number N-1, but is independent of the cyclic stress amplitude. Based on the analysis, a new EPWP increment model for saturated Nanjing fine sand is developed from tested data fitting, which provides a better prediction of the curves of EPWP generation, the number of cycles required for initial liquefaction and the liquefaction resistance.